On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings

Let be a commutative semiring. We define a proper ideal of to be 2-absorbing (resp., weakly 2-absorbing) if (resp., ) implies or or . We show that a weakly 2-absorbing ideal with is 2-absorbing. We give a number of results concerning 2-absorbing and weakly 2-absorbing ideals and examples of weakly 2-absorbing ideals. Finally we de ne the concept of 0 - (1-, 2-, 3-)2-absorbing ideals of and study the relationship among these classes of ideals of .